Generate data for Generalised Linear Models under model misspecification scenario

Function to simulate big data under Generalised Linear Models for the model misspecification scenario through any misspecification type.

Usage

GenModelMissGLMdata(N,X_Data,Misspecification,Beta,Var_Epsilon,family)

Arguments

N: the big data size
X_Data: a matrix for the covariate data
Misspecification: a vector of values for the misspecification
Beta: a vector for the model parameters, including the intercept and misspecification term
Var_Epsilon: variance value for the residuals
family: a character vector for "linear", "logistic" and "poisson" regression from Generalised Linear Models

Value

The output of GenModelMissGLMdata gives a list of

Complete_Data a matrix for Y,X and f(x)

Details

Big data for the Generalised Linear Models are generated by the "linear", "logistic" and "poisson" regression types under model misspecification.

References

Adewale AJ, Wiens DP (2009). “Robust designs for misspecified logistic models.” Journal of Statistical Planning and Inference, 139(1), 3--15. Adewale AJ, Xu X (2010). “Robust designs for generalized linear models with possible overdispersion and misspecified link functions.” Computational statistics & data analysis, 54(4), 875--890.

Examples

Beta<-c(-1,0.75,0.75,1); Var_Epsilon<-0.5; family <- "linear"; N<-10000
X_1 <- replicate(2,stats::runif(n=N,min = -1,max = 1))

Temp<-Rfast::rowprods(X_1)
Misspecification <- (Temp-mean(Temp))/sqrt(mean(Temp^2)-mean(Temp)^2)
X_Data <- cbind(X0=1,X_1);

Results<-GenModelMissGLMdata(N,X_Data,Misspecification,Beta,Var_Epsilon,family)

Results<-GenModelMissGLMdata(N,X_Data,Misspecification,Beta,Var_Epsilon=NULL,family="logistic")

Results<-GenModelMissGLMdata(N,X_Data,Misspecification,Beta,Var_Epsilon=NULL,family="poisson")